For traction slip control through brake management, hitherto, the brake control in the wheel brake of the wheel tending to race has been effected in response to one or two predetermined acceleration thresholds. Moreover, a firm slip threshold optionally dependent on the vehicle speed has been used as a criterion for commencement of the traction slip control. Firmly predetermined thresholds of this type are not capable of handling all situations which are likely to occur. In some cases, commencement of the traction slip control is too early, in others far too late.